of Compressors and Turbines (AE 651) Autumn Semester 2009 - - PowerPoint PPT Presentation

Aerodynamics

• f

Compressors and Turbines

(AE 651)

Autumn Semester 2009

Instructor : Bhaskar Roy Professor, Aerospace Engineering Department I.I.T., Bombay e-mail : aeroyia@aero.iitb.ac.in

1

2 2

Axial Turbines

h-s of Axial Turbine Stage

AE 651 - Prof Bhaskar Roy, IITB Lect - 12

AE 651 - Prof Bhaskar Roy, IITB

Axial Turbines

Lect - 12

Isentropic Efficiencies

Total-to-total efficiency, Static-to-static efficiency,

;

0T 0T 0T

ΔT η = ΔT /

T T T T Stator Rotor

ΔT ΔT η = = ΔT ΔT + ΔT

/ / /

3

AE 651 - Prof Bhaskar Roy, IITB

Axial Turbines

Lect - 12

Isentropic Efficiencies

Total-to-static efficiency, Total-to-total isentropic efficiency of the rotor only is,

;

0T 0T TS T Stator Rotor

ΔT ΔT η = = ΔT ΔT + ΔT

/ / /

0-Rotor 02 03 0-Rotor 0-Rotor 02 03

ΔT T -T η = ΔT T -T

/ /

4

Work Done

H = U C +C w w Th 2 3

AE 651 - Prof Bhaskar Roy, IITB

Axial Turbines

Lect - 12

Degree of Reaction Static isentropic enthalpy drop in rotor D.R = isen Static isentropic enthalpy drop in rotor and stator h h rotor rotor = = h h + h rotor stator T / / / / /

Theoretical DoR, Actual DoR,

actual

2 2 V

• V

h h rotor rotor 3 2 D.R = = = h + h h 2h rotor stator T T

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AE 651 - Prof Bhaskar Roy, IITB

Axial Turbines

Lect - 12

Degree of Reaction

2 actual 2 3 isen T 2 3

1- D.R T -T = 1.03, where, = 0 .97 - 0 .98 1- D.R η T -T

/ // /

These are two definitions are related by,

6

where is the thermodynamic loss coefficient The change in DR due to real flow effects is shown below

DR

0.1 0.25 0.35 0.45 0.5

DRact

0.03 0.073 0.226 0.33 0.433 0.485

AE 651 - Prof Bhaskar Roy, IITB

Axial Turbines

Lect - 12

Total heat drop, assuming C1 to be zero, i.e. flow starting from static condition

2 3 0T T

C H = H + 2

T

H

2 3

C 2

is converted to turbine work is the exhaust flow kinetic energy

2 3 0T Th rotor

C H = H .w + 2

Th

H

is the theoretical enthalpy drop

rotor 023-relative 023-relative

w = ΔT

• ΔT /

Rotor loss coefficient,

7

AE 651 - Prof Bhaskar Roy, IITB

Axial Turbines

Lect - 12

This Implies that ,

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2 2 V

• V

3 2 D.R= 2 C3 2H .w 1+ rotor Th 2H .wrotor Th 2 2 C

• C

2 3 H

• Th

2 = 2 C3 2H .w 1+ rotor Th 2H .wrotor Th

AE 651 - Prof Bhaskar Roy, IITB

Axial Turbines

Lect - 12

This Implies that ,

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2 2 V

• V

3 2 D.R= 2 C3 2H .w 1+ rotor Th 2H .wrotor Th 2 2 C

• C

2 3 H

• Th

2 = 2 C3 2H .w 1+ rotor Th 2H .wrotor Th

AE 651 - Prof Bhaskar Roy, IITB

Axial Turbines

Lect - 12

Assuming that entry velocity is not negligible, i.e.

1 3

C C

2 2 w1 w2 a1 a2 Th 2 2 3 1 rotor Th

C + C C

• C

1 -

• 2.U

2H DR = C - C w 1+ 2H

A simplified DoR as used in Compr is :

t1 t2

C + C Ψ DR = 1 - = 1 - 2.U 2

/

2 2 2 a1 actual actual rotor actual 3 2 Th a2

3

C C DR = DR .w + DR

• cos α

1 - 2H C

/

Combining the two above equations a simplified DR is written:

10

C1 = C3 Ca1=Ca2

AE 651 - Prof Bhaskar Roy, IITB

Axial Turbines

Lect - 12

DR DR

/

Second term is zero, and

rotor

DR ω = DR

/

Ca DR DR 1 = 1- = 1- 2 2 C cos α ω .cos α a rotor 3 3 2 /

11

If, from experience, a certain value of DR is assumed, we get a value of Ca1/Ca2 . If

2 is selected and wrotor is

available from cascade data. The axial velocity ratio found here is the starting point of detailed analysis – and fixing

• f annular flow track

Further simplification may be made If

Net reversible polytropic expansion work = 1-4-3-2-1 =

1 2

v.dp

Total real expansion work

1 2 2 1 2 R 2

C -C = v.dp+ L + 2

Axial Turbines

AE 651 - Prof Bhaskar Roy, IITB Lect - 12

Expansion process is accompanied by internal heat exchange (conversion of irreversible losses LR to QR, internally) and external heat exchange And external heat exchange Irreversible polytropic expansion work

R

Q

q

Q

2 2 poly

1 2 1 1 1 1

k -1 k T

k p H = p .v 1- k - 1 p

1 2 1 1 2

v.dp k = p.dv

Axial Turbines

AE 651 - Prof Bhaskar Roy, IITB Lect - 12

1 2 2 1 2

p ln p k = v ln v

Again, for all practical considerations, k1 = k2 =k. In aircraft turbine generally and or k = 1.28 or 1.29, which tend to go up in the rear stages, as temperature drops. The relation between and k is given by :

R q R q R q R q

∂Q ± ∂Q

• 1
• 1

1+ . R.dT k = . ∂Q ± ∂Q 1+

• 1 .

R.dT

Axial Turbines

AE 651 - Prof Bhaskar Roy, IITB Lect - 12

1

q R R R

( 1- 2)= ∂Q = 0, ∂Q > 0, L = Q =1- 2 - 3 - 4 -

/ q R q R

( 1- 2 ) ∂Q > 0, ∂Q >

q R q R

1- 2", ∂Q < 0, ∂Q >

Axial Turbines

AE 651 - Prof Bhaskar Roy, IITB Lect - 12